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1. value: 10 points A normal population has a mean of 18 and a standard deviation of 5. (a) Compute the z value associated with 24 (Round your answer to 2 decimal places.) Z (b) What proportion of the population is between 18 and 24? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) Proportion (c) What proportion of the population is less than 13? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) Proportion 2. value: 10 points The number of viewers of American Idol has a mean of 29 million with a standard deviation of 5 million. Assume this distribution follows a normal distribution. What is the probability that next week's show will: (a) Have between 30 and 34 million viewers? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) Probability (b) Have at least 23 million viewers? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) Probability (c) Exceed 40 million viewers? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) Probability 3. value: 10 points Customers experiencing technical difficulty with their internet cable hookup may call an 800 number for technical support. It takes the technician between 30 seconds to 15 minutes to resolve the problem. The distribution of this support time follows the uniform distribution. (a) What are the values for a and b in minutes? (Do not round your intermediate calculations. Round your answer to 1 decimal place.) a b ________________________________________ (b-1) What is the mean time to resolve the problem? (Do not round your intermediate calculations. Round your answer to 2 decimal places.) Mean (b-2) What is the standard deviation of the time? (Do not round your intermediate calculations. Round your answer to 2 decimal places.) Standard deviation (c) What percent of the problems take more than 5 minutes to resolve? (Do not round your intermediate calculations. Round your answer to 2 decimal places. Omit the "%" sign in your response.) Percent % (d) Suppose we wish to find the middle 50 percent of the problem-solving times. What are the end points of these two times? (Do not round your intermediate calculations. Round your answers to 3 decimal places.) End point 1 End point 2 4. value: 10 points Among U.S. cities with a population of more than 250,000 the mean one-way commute to work is 24.3 minutes. The longest one-way travel time is New York City, where the mean time is 38.9 minutes. Assume the distribution of travel times in New York City follows the normal probability distribution and the standard deviation is 7.9 minutes. (a) What percent of the New York City commutes are for less than 30 minutes? (Round the intermediate values to 2 decimal places. Round your answers to 2 decimal places. Omit the "%" sign in your response.) Percent % (b) What percent are between 30 and 34 minutes? (Round the intermediate values to 2 decimal places. Round your answers to 2 decimal places. Omit the "%" sign in your response.) Percent % (c) What percent are between 30 and 41 minutes? (Round the intermediate values to 2 decimal places. Round your answers to 2 decimal places. Omit the "%" sign in your response.) Percent % 5. value: 10 points Assume that the mean hourly cost to operate a commercial airplane follows the normal distribution with a mean of $2,300 per hour and a standard deviation of $220. What is the operating cost for the lowest 5 percent of the airplanes? (Round z value to 2 decimal places. Omit the "$" sign in your response.) Operating cost $ 6. value: 10 points For the most recent year available, the mean annual cost to attend a private university in the United States was $20,157. Assume the distribution of annual costs follows the normal probability distribution and the standard deviation is $4,425. Ninety-five percent of all students at private universities pay less than what amount? (Round z value to 2 decimal places and your final answer to the nearest whole number. Omit the "$" sign in your response.) Amount $ 7. value: 10 points The manufacturer of a laser printer reports the mean number of pages a cartridge will print before it needs replacing is 12,325. The distribution of pages printed per cartridge closely follows the normal probability distribution and the standard deviation is 695 pages. The manufacturer wants to provide guidelines to potential customers as to how long they can expect a cartridge to last. How many pages should the manufacturer advertise for each cartridge if it wants to be correct 95 percent of the time? (Round z value to 2 decimal places. Round your answer to the nearest whole number.) Pages 8. value: 10 points Assume a binomial probability distribution with and . Compute the following: (Round all z values to 2 decimal places.) (a) The mean and standard deviation of the random variable. (Round your "?" to 4 decimal places and mean to 1 decimal place.) ? ? (b) The probability that X is 23 or more. (Use the rounded values found above. Round your answer to 4 decimal places.) Probability (c) The probability that X is 15 or less. (Use the rounded values found above. Round your answer to 4 decimal places.) Probability 9. value: 10 points Dottie's Tax Service specializes in federal tax returns for professional clients, such as physicians, dentists, accountants, and lawyers. A recent audit by the IRS of the returns she prepared indicated that an error was made on 11 percent of the returns she prepared last year. Assuming this rate continues into this year and she prepares 52 returns. What is the probability that she makes errors on: (a) More than 6 returns? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) Probability (b) At least 6 returns? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) Probability (c) Exactly 6 returns? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) Probability,8. INCOMPLETE value: 10 points Assume a binomial probability distribution with n = 60 pi= 0.32 . Compute the following: (Round all z values to 2 decimal places.) (a) The mean and standard deviation of the random variable. (Round your "?" to 4 decimal places and mean to 1 decimal place.) ? ? (b) The probability that X is 23 or more. (Use the rounded values found above. Round your answer to 4 decimal places.) Probability (c) The probability that X is 15 or less. (Use the rounded values found above. Round your answer to 4 decimal places.) Probability Question needed n & pi information. Also, Question 7 & 9 are incorrect. Can you please look at it? Thanks,(e) As part of her report to the president, the director of communications would like to report the length of the longest (in duration) 3 percent of the calls. What is this time? (Round z-score computation to 2 decimal places and your final answer to 2 decimal places.) Duration missing

Paper#13448 | Written in 18-Jul-2015

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